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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (7): 89-99.doi: 10.6040/j.issn.1671-9352.0.2018.588

• • 上一篇    

一类具有随机效应的SIRI传染病模型的定性分析

高建忠,张太雷*   

  1. 长安大学理学院, 陕西 西安 710064
  • 发布日期:2019-06-27
  • 作者简介:高建忠(1991— ), 男, 硕士研究生, 研究方向为常微分方程及其应用. E-mail: gaojianzhong2017@126.com*通信作者简介:张太雷(1980— ), 男, 博士,教授, 研究方向为常微分方程及其应用. E-mail: t.l.zhang@126.com
  • 基金资助:
    国家自然科学基金资助项目(11701041);陕西省自然科学基础研究计划项目(2018JM1011;2017JQ1014)

Qualitative analysis of an SIRI epidemic model with stochastic effects

GAO Jian-zhong, ZHANG Tai-lei*   

  1. School of Science, Changan University, Xian 710064, Shaanxi, China
  • Published:2019-06-27

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摘要： 研究了具有随机效应的SIRI双线性传染病模型。利用停时理论及Lyapunov分析方法, 证明了随机模型正解的全局存在唯一性和有界性, 讨论了随机模型的解在相应确定性模型的无病平衡点和地方病平衡点附近的振荡行为, 得到了随机模型的解的平均持续和疾病灭绝的充分条件。最后, 数值模拟验证了理论结果的正确性。

关键词: 随机SIRI模型, 振荡行为, 平均持续, 疾病灭绝

Abstract: An SIRI bilinear epidemic model with stochastic effects is studied. The global existence, uniqueness and boundedness of its positive solution are proved by using stopping time theory and Lyapunov analysis method. It is also shown that the solution of the stochastic model oscillates around the corresponding deterministic disease-free equilibrium and endemic equilibrium points, and the sufficient conditions for persistence in mean of the solution of the stochastic model and disease extinction are obtained. Finally, numerical simulations are carried out to prove the validity of theoretical results.

Key words: stochastic SIRI model, oscillating behavior, persistence in mean, disease extinction

中图分类号: 

  • O175.1
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